Turnover as an Actuarial Assumption on its own
by Dr K Heubeck (Germany)
As a n m m s private pnsion plans the actuary i s used to take into
account not only m r t a l i t y but also other basic assmptions such as
the probability t o becane disabled or the m r i a g e probability. 4
further basic i t e m is turnwer meaning the prohbility to withdraw
from the plan population with or without vest& rights but without
benefits falling due h e l i a t e l y . This force of decrenent i s not a
matter of a x p r a b l y systeinatic concern in a l l m t r i e s and is
taken into account in calculations m s t differentially.
I n Germany, for example, private ,ension plan calculations for tax
purposes have taken and s t i l l take into account turnwer on a global
basis only by excluding all those younger than age 30 and including
a l l those over age 30 on a 100 % basis. This approach had proved to
provide for rather g a d average figures and had gained ground also
for accounting purposes.
B u t for m y kinds of valuations, for example those yith regard to
the purchase of a canpany, a m r e sophisticated approach giving a
better description of the real turnover situation i n the ccarp3any
mncerned has been utilized; sawtimes even a different calculation
method has been used.
Of course, also valuations w i t h respect to US-American and other
standards
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particular importance for ewmple FAS 87 and Internal
Revenue Code (IRC) section 404 A
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problem of an appropriate consideration of turnover in the canpany's
plan population. With regard to Germn tax purposes, the Federal Tax
Court (BFM) just recently enforced a direct explicit and thus
non-global consideration of turnover S& with regard to a different
subject: t h e accumulation of reserves f o r long-service awards to
employees. The C n u r t duely wrks f r m t h e principle t h a t prefunding
i s necessary only insofar as t h e obligation to provide f o r this kind
of pyments does not cease to e x i s t due to the q l o y e e ' s
t e ~ m i n a t i o nbefore the award w i l l f a l l due.
Thus an appropriate a n s i d e r a t i o n of turnover is of cardinal impor-
tance. In lack of h i s t o r i c a l ex.perience and i n ,px-ticular
i n lack of
suitable oxnpany s t a t i s t i c s m e could try to find a rasonable solut i o n through tm wayz:
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supplement of the by ncw existing accounting basis by turnover as
an additional decrenent force i n an a c t u a r i a l l y correct way.
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use and s t e p by step improvercent of existing turnover s t a t i s t i c s
on ampmies' plan p l a t i o n and realization of proceedings
understandable also by non-experts
.
I l i k e t o i n v i t e t o discuss my following remarks, of course hopand J a w i n g f o r certain to g e t useful suggestions and criticism £ran
international colleagues nu& more experienced in this f i e l d .
2. W
e
d Basic Probabilities
The first way mentioned shculd be realizaSle quite easily. The
camon calculations neglecting turnover are based on decrenent
probabilities ( l e t ' s say q) f o r the mortality of the a c t i v e subpopllation (qa), of pensioners, of t h e t o t a l plan population (q)
and f o r becaning disabled (i). These prokabilities a r e defined and
derived not independent from each other, but in case of isolated
derivation they are assto be independent of the turnover probability (s).
considering the tunuxrer probability
~t is well-knom, in a -11
as an additional decrenent force the original decrement probabilities q have to be modified accordingly:
q m y also mean qa or i. Already £ran a practical point of view
me has to override argments that s can be measured only conditionally (nut independent) but is used as being independent. A m&
mare severe problem is that with regard to turnaver s similar differentiations as made w i t h regard to the other decrement probabilities
are neither possible nor necessary. Not only for historical reasons,
mrtality and disability are measured in terms of age. As concerns
sex actuaries had to learn fran a new doctrine of salvation (Heilslehre) to which extent we are still allawed to say: vive la petite
difference. But as concerns turnover, it is most obvious that also
other amditions such as years of service rendered in the m y ,
should be registered and incorporated in the nodell and the
valuation in a suitable manner.
Any routinist will suspect that turnover is less dependent on age or
sex than on canpany years of service rendered by the employee, on
bran& of industry and location, on the gxlncmic situation and
unanployment or other norr-personal factors. The actuary is asked to
select the essence and to determine and to make use of a a l u m of
figures describing the situation as good as possible and as accurate
as necessary. hreryone lam& such an attempt is rnost amplicated i f
not a lost case looking to the efforts and the lack of sense one has
to face trying t o set up such detailed statistics in a anpry.
With regard to this background it should mke sense to look for
another solution easy to handle in practice and which guarantees
reasonable results. Starting the problem one
vmrk £ran the fact
that rrrost canpanies lcnw a t least one figure characterizing their
turnover situation; that is the overall turnover telling about the
portion of' employees withdrawing throughout the year without benef i t s falling due. This ratio, in percent, i s available for most
a m p r i e s or can be obtained easily. In any case, new additions and
withdrawals within the year should be disregarded. As concerns this
kind of overall turnover one can define differ*
turnover-levels,
for example:
level
overall turnover
Classifying a ccmpany by its overall turnover rate defines its relation to other axpmies
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less nor m e . As long as no
additional information is available it i s of rather no avail to
speculate £or further differentiations of dependencies, for devia-
tions out of the p~oportiono r less proportiomte, or for anything
similar. This holds true in particular as many of these aspects only
have a minor impact on the results of calculatiors.
As a consequence one is in need of a mark, a standard/ncdell onpany
that has mre or less artificially but credibly designed t m e r
prokabilities serving as a measure for all cases of application.
Based cn a large body of canpany statistics and specific investigations we have tried to derive su& standard turnover rates. It has
turned up by the way really not surprising - that turnover mainly
depends an the employees' years of service rendered.
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The following draft tells about the profile of such determined
standard turnover probabilities.
?he cfioice of the appropriate level of w e r a l l turnover (as
mentioned before) i s of decisive importance. Nevertheless, w x k h g
£ran the overall turnaver situation of plan popllation one has to
pay attention to both an internal and external dependence on time.
The internal dependence is due to the changing service structure of
a given ppulation: even i f tumwer frequencies remain undmnged
w i t h regard to the individual case, the averall turnover situation
of a p l a t i o n being "ycung" with regard to service already
rendered is higher than that of a population w i t h "mtured" service.
The external dependency results fmn the j& market and the ampany's manpwer need. Thus any overall tumover actually observed
needs to be adjusted w i t h regard to these internal and external
effects before assigning the corresponding turnover level.
Each turnover level relates to a weight factor to be applied to the
standard turnover probabilities. The thus obtained probability
rates, d f i e d according to the weight fa-,
can be used to
recalculate the other &sic probabilities according to the formla
mentioned. By this, probabilities for a l l forces of decrement
necessary for the valuation are an hand.
Turnover probabilities depending an s w i c e years and the rates for
the other forces of decremnt depending on age give r i s e to a
2-dimensional decrement table mnpared to our calculations
hitherto based an a one-dimslsional decrement table t h i s rtleans a
substantial ccmplicatian.
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These practical problems give cause to think about sbplifying
methods even in the era of m p u t e r s . One possible solution could be
to prepare valuations f i r s t without taking into account any tummer
assmptions and in a second step adjusting the results through a
factor depending only an service and tummer level. This factor
could be determined and tabulated once, based on the actuarial
cost mi3d that is used and the benefits to be valued.
Corresponding investigations with regard to an appropriate valuation
a pranising light on this approach.
of 1-service
awards
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